My sewage system is way in the green for capacity (76.1 needed, 123.0 capacity). Yet every now and then I get a yellow alert that I have "backed up pipes", and the Treatment Plant shows the "Sewage Problems!" icon. No problems are apparent aside from the yellow alert; the plant has never lost power, and as far as I'm aware there has never been a lack of workers. The alert stays for a few minutes and goes away on its own with no apparent cause. I've had this issue in every city once it reached a certain point. What is the deal here?
I agree with Robotnik in the comments, its probably Rush hours causing this. Have another Treatment tank in the plant but keep it deactivated to save money. Then activate it when rush hour occurs. Also check the roads leading to the plant, is there no way you can create a bit of a "shortcut" for further laying areas.
If all else has failed (your roads are all connected, you've eliminated all pollution, and you have tons of free capacity) your sewage plant may be too far away (in road-driving distance). If that's the case, the buildings with the longest driving distance to your plant will not be serviced or service will be spotty. Move the plant closer along the road, or add another one nearby.